31 Tone Equal Temperament

Harmonic Context in 31 Tone Equal Temperament

Harmonic context is one of the most important concepts in harmony, and one that is often under-emphasized in the study of music theory and tonal systems. Harmonic context is a broad concept, and encompasses many different sorts of cues, such as melodic, harmonic, and cultural.

In single chords

One can talk about harmonic context even in simple cases, such as when looking at an isolated chord. Intervals with more harmonic strength tend to define or dominate the overall context of the chord. As an example, a chord containing exactly one perfect fifth, or a chord with doubled octaves, tends to strongly imply the bottom note of the fifth (or octave) as root; the other, weaker intervals in the chord are then interpreted by the ear in this context.

Harmonic context becomes a more useful and important concept, however, in cases of chords or intervals that are harmonically ambiguous. A good example from the familiar 12-ET tuning is the tritone: this interval, a perfect division of the octave in half, is harmonically ambiguous and does not imply any note as a tonal center. However, in Western music, the tritone occurs most often in the context of a dominant seventh chord. A tritone, played on its own, that fits into the dominant seventh chord of the key in a song or piece that has the standard Western tonality, will tend to be perceived as having a tonal center associated with the dominant seventh chord in the key. The harmonic context gives an otherwise rootless interval a clear root or tonal center.

Melody providing harmonic context

Harmonic context can also be provided or implied by melodies: a major scale provides a strong harmonic context for a tonal center, with the root of the scale. This context is reinforced by the natural harmonic series, as the root, second, third, fifth, and seventh of a major scale all match natural harmonics (8,9,10,12,15) but is also influenced by cultural and other contextual cues: music in different modes demonstrates that the same combination of notes can imply different tonal centers.

Differences in 31-ET

In 31-ET, harmonic context is far more complex. 31-ET contains six intervals (twelve counting inversions) which can be harmonically ambiguous. The whole tone, the building block of most modern Western music, is more ambiguous in 31-ET than 12-ET.